Transverse $\mathcal F^T$-entropy and transverse Ricci flow for Riemannian foliations
Differential Geometry
2022-09-20 v2
Abstract
In this paper, we introduce an entropy functional on Riemannian foliation, inspired by the work of , which is monotonically along the transverse Ricci flow. We relate their gradient flow, via diffeomorphism preserving the foliated structure of the manifold with Riemannian foliation, to the transverse Ricci flow. Moreover, inspired by the work of Fuquan Fang and Yuhao Zhang, we give a necessary condition for codimension 4 Riemannian foliation admitting the transverse Einstein metric.
Keywords
Cite
@article{arxiv.2104.10945,
title = {Transverse $\mathcal F^T$-entropy and transverse Ricci flow for Riemannian foliations},
author = {Dexie Lin},
journal= {arXiv preprint arXiv:2104.10945},
year = {2022}
}
Comments
13 pages